摘要
设Pn和Cn分别是n个顶点的路和圈,用Sk*n+1表示把kPn+1的每个分支的一个1度点重迭在一起得到的图,ωδ(δ=rm+1)表示把rCm+1中每个分支的一个1度点重迭后得到的图,并用Vω(kn+1)δ表示把图Sk*n+1的kn+1个顶点与(kn+1)ωδ的每一个分支的2r度点依次重迭后得到的图。运用图的伴随多项式的性质,证明了Vωxδ∪yωδ(x,y∈N)形图簇的伴随多项式的因式分解定理,进而证明了这类图簇的补图的色等价性。
Let Pn be the path with n vectices and let Cn be the cycle with n vectices,and let S＊kn＋1 be the graph consisting of kPn＋1 by coinciding the vertex of degree 1 of each component of kPn＋1 respectively;and let ωδ be the graph consisting of rCm＋1 by coinciding one vertiex of degree 2 of each component of rCm＋1.respectively;and let Vω（kn＋1）δ be the graph obtained from S＊kn＋1 and（kn＋1）ωδ by coinciding each vertex of S＊kn＋1 with the vertex of degree 2r of every component of,respectively.Applying the properties of adjoint polynomials,we prove that factorization theorem of adjoint polynomials of theVωxδ∪yωδ（x,y∈N）-shaped graphs,where δ=rm＋1 and x,y∈N.Furthermore,we obtain the structure characteristics of chromatically equivalent graphs of their complements.
出处
《南昌大学学报（理科版）》
CAS
北大核心
2010年第2期111-116,共6页
Journal of Nanchang University(Natural Science)
基金
国家自然科学基金资助项目(10671008)
关键词
色多项式
伴随多项式
因式分解
色等价性
chromatic polynomial
adjoint polynomials
factorization
chromatically equivalence
